On testing variance components in unbalanced mixed linear model

Lýdia Širková; Viktor Witkovský

Applications of Mathematics (2001)

  • Volume: 46, Issue: 3, page 191-213
  • ISSN: 0862-7940

Abstract

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The paper presents some approximate and exact tests for testing variance components in general unbalanced mixed linear model. It extends the results presented by Seifert (1992) with emphasis on the computational aspects of the problem.

How to cite

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Širková, Lýdia, and Witkovský, Viktor. "On testing variance components in unbalanced mixed linear model." Applications of Mathematics 46.3 (2001): 191-213. <http://eudml.org/doc/33083>.

@article{Širková2001,
abstract = {The paper presents some approximate and exact tests for testing variance components in general unbalanced mixed linear model. It extends the results presented by Seifert (1992) with emphasis on the computational aspects of the problem.},
author = {Širková, Lýdia, Witkovský, Viktor},
journal = {Applications of Mathematics},
keywords = {unbalanced mixed linear model; variance components; Wald test; ANOVA-like test; Bartlett-Scheffé tests; unbalanced mixed linear model; variance components; Wald test; Bartlett-Scheffé test},
language = {eng},
number = {3},
pages = {191-213},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On testing variance components in unbalanced mixed linear model},
url = {http://eudml.org/doc/33083},
volume = {46},
year = {2001},
}

TY - JOUR
AU - Širková, Lýdia
AU - Witkovský, Viktor
TI - On testing variance components in unbalanced mixed linear model
JO - Applications of Mathematics
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 46
IS - 3
SP - 191
EP - 213
AB - The paper presents some approximate and exact tests for testing variance components in general unbalanced mixed linear model. It extends the results presented by Seifert (1992) with emphasis on the computational aspects of the problem.
LA - eng
KW - unbalanced mixed linear model; variance components; Wald test; ANOVA-like test; Bartlett-Scheffé tests; unbalanced mixed linear model; variance components; Wald test; Bartlett-Scheffé test
UR - http://eudml.org/doc/33083
ER -

References

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  1. The distribution of a linear combination of chi-square random variables, J. Roy. Statist. Soc. Ser. C 29 (1980), 323–333. (1980) 
  2. Testing for hypothesis in mixed linear models with two variance components, Listy Biometryczne—Biometrical Letters 29 (1992), 13–31. (1992) 
  3. 10.1080/02331889408802446, Statistics 25 (1994), 213–223. (1994) MR1366826DOI10.1080/02331889408802446
  4. 10.1093/biomet/48.3-4.419, Biometrics 48 (1961), 419–426. (1961) Zbl0136.41103MR0137199DOI10.1093/biomet/48.3-4.419
  5. Statistical Tests for Mixed Linear Models, J. Wiley, New York, 1998. (1998) MR1601351
  6. 10.1080/03610928808829680, Comm. Statist. Theory Methods 17 (1988), 1287–1309. (1988) MR0942977DOI10.1080/03610928808829680
  7. 10.1080/03610928808829675, Comm. Statist. Theory Methods 17 (1988), 1135–1164. (1988) MR0942972DOI10.1080/03610928808829675
  8. 10.1080/01621459.1991.10475018, J. Amer. Statist. Assoc. 86 (1991), 179–187. (1991) MR1137109DOI10.1080/01621459.1991.10475018
  9. Optimum invariant tests in mixed linear models with two variance components, In: Statistical Data Analysis and Inference (Y. Dodge, ed.), North-Holland, Amsterdam, 1989, pp. 381–388. (1989) Zbl0735.62068MR1089650
  10. 10.1080/02331889708802533, Statistics 27 (1996), 297–310. (1996) MR1375446DOI10.1080/02331889708802533
  11. 10.1214/aos/1176351065, Ann. Statist. 16 (1988), 1727–1740. (1988) MR0964950DOI10.1214/aos/1176351065
  12. 10.1214/aos/1176343586, Ann. Statist. 4 (1976), 878–890. (1976) MR0418345DOI10.1214/aos/1176343586
  13. 10.1016/0047-259X(71)90001-7, J. Multivariate Anal. 1 (1971), 257–275. (1971) MR0301869DOI10.1016/0047-259X(71)90001-7
  14. Estimation of Variance Components and Applications, North-Holland Publishing Company, Amsterdam, 1988. (1988) MR0933559
  15. Applying Wald’s variance component test, Ann. Statist. 11 (1983), 197–201. (1983) MR0684876
  16. 10.1080/02331888508801898, Statistics 16 (1985), 621–635. (1985) Zbl0593.62066MR0803502DOI10.1080/02331888508801898
  17. 10.1016/0378-3758(92)90086-8, J. Statist. Plann. Inference 30 (1992), 257–266. (1992) Zbl0746.62016MR1157765DOI10.1016/0378-3758(92)90086-8
  18. 10.1214/aoms/1177731946, Ann. Statist. 11 (1940), 96–100. (1940) MR0001502DOI10.1214/aoms/1177731946
  19. 10.1214/aoms/1177730350, Ann. Statist. 18 (1947), 586–589. (1947) Zbl0029.30703MR0023498DOI10.1214/aoms/1177730350
  20. 10.1214/aos/1176347019, Ann. Statist. 17 (1989), 318–326. (1989) Zbl0669.62055MR0981453DOI10.1214/aos/1176347019
  21. Optimality of the ANOVA-like test in model with two variance components, In: MEASUREMENT 99. Proceedings of the International Conference on Measurement, Smolenice, Slovak Republic, 26–29 April 1999, I. Frollo, A.  Plačková (eds.), 1999, pp. 28–31. (1999) 

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